Humboldt-Universität zu Berlin - Mathematisch-Naturwissen­schaft­liche Fakultät - International Research Training Group 1740


Project D1: Auto- and cross-correlations in hierarchical modular networks of spiking neurons with self-sustained and irregular activity

Research Team: L. da F. Costa (USP), B. Lindner (HUB), A. Roque (USP), S. Rüdiger (HUB), M. Zaks (UP)

Outline: At a macroscopic scale the architecture of cellular connections in the cortex is hierarchical and modular with dense local connectivity and sparse long-range connectivity between modules. At the resting state of the brain the cortex displays self-sustained activity characterized by irregular neuronal firing and spontaneous synchronous transitions between distinct high and low activity states (up and down states). Although the properties of cortical self-sustained activity depend on the organization of cortical connectivity and the individual cortical components, the precise nature of the contributions of network topology and the intrinsic firing properties is currently not known. Recently, Roque and colleagues used a computational model of the cortex to study the interplay between macroscopic topology and composition in terms of neurons of different intrinsic firing behaviors. They studied hierarchical and modular networks made of neurons belonging to the five main electrophysiological cell classes in the cortex: regular spiking, chattering and intrinsically bursting neurons (all excitatory), and fast spiking and low threshold spiking neurons (all inhibitory). The networks displayed transiently chaotic self-sustained activity states whose lifetime depends on network modularity, mixture of neurons of different types and excitatory and inhibitory synaptic strengths. The states with longest lifetime expectations in the region of phase space with physiologically plausible mean network firing rates displayed collective behavior that resembles up and down states. An analytical approach to these distinct dynamical regimes may be possible by applying approximations recently developed in the Lindner group. Here a self-consistent single-neuron-simulation scheme was introduced to study the second-order correlation statistics (spike train power spectra) in a large sparse and homogeneous network of spiking neurons. This scheme can be extended to cases of (i) heterogeneous networks; (ii) different connection topology; (iii) smaller or more densely connected networks with substantial cross-correlations among neurons. All cases are relevant to hierarchical modular networks and will not only lead to efficient numerical schemes for the second-order statistics but moreover suggest novel analytical approaches to the calculation of spike train statistics in recurrent networks of spiking neurons.

Research within the Brazilian group (PhD Supervisor: A. C. Roque): The hierarchical modular network will be made more realistic by adding the following elements: (i) a layered structure to each module with connectivity pattern representing local cortical circuitry; and (ii) synaptic strength modification rules to implement synaptic plasticity phenomena. Also planned is the elaboration of a reduced system that can capture the main features of the dynamic behavior of a network module, comprised by mixed populations of different neuron types, which can be used in the construction of more cost-effective large-scale computational models or for mean-field analyses of the models.

Research within the German group (PhD Supervisor: B. Lindner): We will start with the simple case of three large sparse populations and employ different approaches to describe the (i) firing rates of the populations, in particular, the time-dependent mean activity of each population and (ii) the spike train cross- and power spectra. To this end, we will employ standard approximations including rate equations, the Fokker-Planck approach based on the diffusion approximation, but also the above-mentioned self-consistent scheme that couples the spike train power and cross-spectra of the distinct population with each other. Robust predictions of the analytical approximations and of the numerical self-consistent scheme can then be tested in large-scale computer simulations done by the Brazilian group. A particular focus will be on the emergence of slow processes in the modular network and the corresponding behavior of spectral measures at low frequencies.